A279198 Number of pairs of conjugate inseparable solutions of X + Y = 2Z (integer, disjoint triples from {1,2,3,...,3n}).

0, 0, 0, 2, 7, 52, 297, 1994, 14594, 113794, 991741, 9199390, 94105010, 1015012796, 11914379971, 146974330141, 1954701366709

Offset: 1

Author

N. J. A. Sloane, Dec 15 2016

Keywords

• nonn
• more

Examples

			Richard Guy gives examples in his letter.
		

References

• R. K. Guy, Sedlacek's Conjecture on Disjoint Solutions of x+y= z, Univ. Calgary, Dept. Mathematics, Research Paper No. 129, 1971.
• R. K. Guy, Sedlacek's Conjecture on Disjoint Solutions of x+y= z, in Proc. Conf. Number Theory. Pullman, WA, 1971, pp. 221-223.
• R. K. Guy, Packing [1,n] with solutions of ax + by = cz; the unity of combinatorics, in Colloq. Internaz. Teorie Combinatorie. Rome, 1973, Atti Conv. Lincei. Vol. 17, Part II, pp. 173-179, 1976.
• Nowakowski, Richard Joseph, Generalization of the Langford-Skolem problem, MS Thesis, University of Calgary, 1975.

Links

• R. K. Guy, Letter to N. J. A. Sloane, June 24 1971: front, back [Annotated scanned copy, with permission] See sequence "J".
• R. J. Nowakowski, Generalizations of the Langford-Skolem problem, M.S. Thesis, Dept. Math., Univ. Calgary, May 1975. [Scanned copy, with permission.]

Crossrefs

All of A279197, A279198, A202705, A279199, A104429, A282615 are concerned with counting solutions to X+Y=2Z in various ways.

See also A002848, A002849.

Formula

A279197(n) + 2*A279198(n) = A202705(n).

Extensions

a(7)-a(16) from Fausto A. C. Cariboni, Feb 27 2017

a(17) from Fausto A. C. Cariboni, Mar 22 2017